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Medical-image Analysis and Statistical Interpretation Lab

Robust Estimation of Spatially Variable Noise Fields

Posted by on Monday, August 31, 2009 in Noise Estimation.

B. A. Landman, P-L Bazin, S. A. Smith, and J. L. Prince, “Robust Estimation of Spatially Variable Noise Fields”, Magnetic Resonance in Medicine, Aug;62(2):500-9. 2009 PMC2806192

Full text: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2806192/

Abstract

Consideration of spatially variable noise fields is becoming increasing necessary in magnetic resonance imaging given recent innovations in artifact identification and statistically-driven image processing. Fast imaging methods enable study of difficult anatomical targets and improve image quality but also increase the spatial variability in the noise field. Traditional analysis techniques have either assumed that the noise is constant across the field of view (or region of interest) or have relied on separate magnetic resonance image acquisitions to measure the noise field. These methods are either inappropriate for many modern scanning protocols or are overly time-consuming for already lengthy scanning sessions. We propose a new, general framework for estimating spatially variable noise fields from related, but independent magnetic resonance scans which we call noise field equivalent scans. These heuristic analyses enable robust noise field estimation in the presence of artifacts. Generalization of noise estimators based on uniform regions, difference images, and maximum likelihood are presented and compared with the estimators derived from the proposed framework. Simulations of diffusion tensor imaging and T2-relaxometry demonstrate a ten-fold reduction in mean squared error in noise field estimation, and these improvements are shown to be robust to artifact contamination. In vivo studies show that spatially variable noise fields can be readily estimated with typical data acquired at 1.5T.

Simulated impact of thresholds on bias in SVNF estimation. 5,000 Monte Carlo iterations were performed for each of 10 Rician distributed observations and for each of 40 linearly spaced SNRs between 1:2 and 20:1. For each dataset, the SVNF was estimated using Eq. (7) with a threshold of 0:1 (no threshold), 3:1, 5:1, and by Eq. (8) (data-adaptive threshold). Second, 5,000 Monte Carlo draws of 1 Rayleigh distributed observation (i.e., an “outlier” with a Rician distribution with SNR=0:1) and 9 Rician distributed observations for each of 40 linearly spaced SNRs between 1:2 and 20:1. For each dataset, the SVNF was estimated using Eq. (7) with a threshold of 0:1 (no threshold), 3:1, 5:1, and by Eq. (8) (data-adaptive threshold). The standard error on all reported estimates is less than 0.005 (for clarity, error bars are not shown).
Simulated impact of thresholds on bias in SVNF estimation. 5,000 Monte Carlo iterations were performed for each of 10 Rician distributed observations and for each of 40 linearly spaced SNRs between 1:2 and 20:1. For each dataset, the SVNF was estimated using Eq. (7) with a threshold of 0:1 (no threshold), 3:1, 5:1, and by Eq. (8) (data-adaptive threshold). Second, 5,000 Monte Carlo draws of 1 Rayleigh distributed observation (i.e., an “outlier” with a Rician distribution with SNR=0:1) and 9 Rician distributed observations for each of 40 linearly spaced SNRs between 1:2 and 20:1. For each dataset, the SVNF was estimated using Eq. (7) with a threshold of 0:1 (no threshold), 3:1, 5:1, and by Eq. (8) (data-adaptive threshold). The standard error on all reported estimates is less than 0.005 (for clarity, error bars are not shown).

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